Barycenter curvature-dimension condition for extended metric measure spaces

2025/01/27 by Han, Bang-Xian, Liu, Deng-yu, Zhu, Zhuo-nan
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2502.06793

Abstract

In this survey, we introduce a new curvature-dimension condition for extended metric measure spaces, called Barycenter-Curvature Dimension condition BCD, from the perspective of Wasserstein barycenter.

Related

• On the geometry of Wasserstein barycenter I
• On the geometry of metric measure spaces with variable curvature bounds
• Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces
• Local curvature-dimension condition implies measure-contraction property
• Example of an Highly Branching CD Space